Question

How many solutions are there to this equation?
4x - 6 + 3(2-x) = 2x - (x - 4)

A, no solution

B. exactly one solution

C. at least two solutions

D. infinitely many solutions

Answer 1

Step-by-step explanation:

4x - 6 + 3(2 - x) = 2x - (x - 4)

4x - 6 + 6 - 3x = 2x - x + 4

x = x + 4

0 = 4

Since 0 = 4 is a false statement, there are no real solutions for x. (A)

Answer 2

Option D is correct. Since x tends to infinity hence x has infinitely many solutions

Equations are expressions separated by an equal sign.

Given the equation

$4x - 6 + 3(2-x) = 2x - (x - 4)$

Expand the brackets using distributive law:

$4x - 6 + 6-3x = 2x - x + 4$

Collect the like terms:

$4x -2x+x-3x = 4+6-6\\2x-2x=4\\0x = 4\\x = \frac{4}{0}\\x=\infty$

This shows that x has infinitely many solutions

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